Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20259350 | C2 | semidirect |
| 2. C2×#20259347 | C2 | semidirect |
| 3. #27133209 | C2 | semidirect |
| 4. C2×#20259284 | C2 | semidirect |
| 5. #27132881 | C2 | semidirect |
| 6. #27132877 | C2 | semidirect |
| 7. #27132867 | C2 | semidirect |
| 8. #27132857 | C2 | semidirect |
| 9. #27132686 | C2 | semidirect |
| 10. #27132662 | C2 | semidirect |
| 11. #417×C191 | C2 | semidirect |
| 22. #20259320 | C22 | semidirect |
| 23. #20259318 | C22 | semidirect |
| 24. #20259311 | C22 | semidirect |
| 25. #20259309 | C22 | semidirect |
| 36. Dic191⋊C8 | C22 | semidirect |
| 37. Dic191⋊C8 | C22 | semidirect |
| 38. #20259245 | C22 | semidirect |
| 39. #20259242 | C22 | semidirect |
| 43. #103×C191 | C22 | semidirect |
| 44. #102×C191 | C22 | semidirect |
| 51. C2×D764 | D4 | semidirect |
| 158. Dic191 | AGL(1,ℤ/8) | semidirect |
| 166. C191 | #3036 | semidirect |
| 178. #417 | D191 | semidirect |
| 209. #103 | C2×D191 | semidirect |
| 211. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259350 | 2 |
| C2×#20259347 | 2 |
| #27133209 | 2 |
| C2×#20259284 | 2 |
| #27132881 | 2 |
| #27132877 | 2 |
| #27132867 | 2 |
| #27132857 | 2 |
| #27132686 | 2 |
| #27132662 | 2 |
| #417×C191 | 2 |
| #3036 | 191 |